image restoration juan navarro sorroche phys-6314 physics department the university of texas at...

Image Restoration

Juan Navarro Sorroche

Phys-6314

Physics Department

The University of Texas at Dallas

Fall 2010

School of Natural Sciences & MathematicsDepartment of Physics


Image Restoration

1. Motivations for image restoration

2. Pin-hole camera model

3. Sources of image distortion

4. Distortion models

5. Correcting algorithms and implementation

G. Ferioli, R. Jung - LHC-BI Review Workshop November 19&20

LHC Screen Profile Monitors

G. Ferioli, R. Jung

. ( )

. ( )u d d

u d d

x x f r

y y f r

2 41 2

21

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( ) 1

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f r k r

f r k r k r k r k r

2 4 6

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11 ( ) ( ) ( ) ..........

1 ( )kr kr kr

kr


Image Distortion

,u n

,v m2 2 1 2( )r u v

Motivations for image restoration

8’x4’ camera calibration board

Introduction


Image Distortion

Close up view of 8’x4’ camera calibration board

Introduction


Any DAQ system where images are created requires restoration of images

• Oscilloscopes• Microscopes• X-rays machines• Robotic vision• CCD/CMOS sensors• Medical imaging equipment• Ionization chambers• Mass spectrometers• Any projective type of detector

Introduction

Projective Transformation

X

Y

Z

C

wz

wx

wy

wu

v

P

( , , )w w w wP x y zw

w

w

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x u

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w w

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z p m m f y

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( )

( )x

y

u n n p

v m m p

World coordinates to pixels transformation

Pin-Hole Camera ModelSchool of Natural Sciences & MathematicsDepartment of Physics

projection center to image plane distance = focal length

origin of camera reference system world coordinate origin

w f

C

. .

. .

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CCD/CMOS camera sensor pixel’s coordinates n, n0, m, m0 = # of pixelspx, py = pixel size

0

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( )

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y w

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Projective Transformation

X

Y

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wx

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v

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( , , )w w w wP x y zw

w

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World coordinates to pixels transformation: general case


projection center-image plane distance=focal length

origin of camera reference system world coordinate origin

w f

C

0

0

0

0 *

10 0 1

xw

w wy

w

f npn xfz m m yp

z

General expression for the camera transform

xw,yw,zw homogenous 4-vector

K= Camera calibration matrixR=Rotation matrixC=camera center coordinatesP=Projective Transformation matrix

For the case of camera rotation and translation

Pin-Hole Camera Model


Image Distortion Sources

1. Intrinsic

• Radial distortion• Tangential distortion• Skew distortion

2. Extrinsic

• Projection distortion• Perspective distortion• Skew distortion

0 tan( )k m

. uc

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k nn

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k n m n mmk mk

un

um

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pum

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n

m


Image Distortion Sources

Perspective Distortion

Distortion Models


Distortion Correction Models

. ( )

. ( )u d d

u d d

x x f r

y y f r

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2 4 62

11 ( ) ( ) ( ) ..........

1 ( )kr kr kr

kr

. ( )u d dr r f r

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Model

Radial functions

Most used

Best approximation

Easiest. Good approximation

Radial distortion

Perspective distortion ( )

( )

i

i

ic

i

kxx

k y

kyy

k y

c#( , )

tan( )2

v h pixelsk

Commercial packages

AdobeRoboRealmPhotoModellerFireWorks

Open Source

GIMP

Professional metrology

Halcon

Calibration Board Pixel Plot


Correcting Algorithms & Implementation

Radial Points - Fitting Function Plot



Pin-hole Vs. Radial Distortion Corrected Pixel Plot



Pin-hole Vs. Rad/Persp. Corrected Pixel Plot





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Conclusions


Images must be corrected from optical system distortions prior of making any measurement

Radial distortion affects object’s position determination & other derived variables

Perspective distortion can leads to large errors in position determination depending on angle of tilt

Distortions must be removed before ideal (pin-hole) camera transformations are made

Conclusions

image restoration juan navarro sorroche phys-6314 physics department the university of texas at...

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